My guess: probably not. ST will probably set out a range of possible values for c, or outline equations which will function if c is a certain value, or whatever. But I doubt it would mathematically define c to be a specific value as a matter of neccessity.

I don't think c is just set by magnetic properties of the vacuum, and so on. I think that c is a specific property set by the geometry of our particular spacetime, and that the permeability/permitivity constants are effects, rather than causes. But then again, I don't really know.